Following the quantum dynamics of an open-dissipative many-body system
with multiple bosonic and fermionic reservoirs in a nonequilibrium
state, beyond the linear response regime, is a significant theoretical and
computational challenge.
In the realm of molecular
conducting junctions, we should describe the
out-of-equilibrium dynamics of the molecular unit while handling
both electrons and molecular vibrations, accounting for
many-body effects such as electron-electron, phonon-phonon and
electron-phonon interactions.
Given this complexity, studies in this field are mostly focused on
steady-state properties, using e.g., scattering theory
[1]}, [2]}, [3]}, while ignoring vibrational
nonequilibrium effects. Perturbative treatments (in either the
molecule-leads coupling parameter or the electron-phonon interaction
energy) are commonly used, including the nonequilibrium Green's
function technique [4]}, [5]}, [6]}, [7]}, [8]}
and Master equation approaches
[5]}, [10]}, [11]}, [12]}, [13]}, [14]}. For following the
real-time dynamics of such systems, involved methods have been
recently developed, e.g., semiclassical approaches
[15]}, [16]}.
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